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Certified calculator · Version 1

Limit Calculator

Evaluate a supported expression progressively closer to a target point from the left, right or both sides.

Finite limit2
Left estimate2
Right estimate2

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Visual scale

Accessible data view
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CalcuMint Pro

Advanced Analysis

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Advanced chartsExplore the result across time and assumptions.
Scenario comparisonCompare multiple assumptions side by side.
Sensitivity analysisSee which assumptions change the outcome most.
Goal SolverSolve backwards from the outcome you want.
Result methodology

The certified finite-limit engine requires stable one-sided convergence and agreement for a two-sided result.

Solution steps
  1. Parse f(x) = (x^2-1)/(x-1)
  2. Sample progressively closer to x = 1 from both sides
  3. Certified finite limit ≈ 2.000000000001193

How this calculator works

The engine examines shrinking-distance sample sequences and only reports a finite limit when the relevant one-sided samples demonstrate stable convergence.

Formula

limₓ→ₐ f(x) from converging one-sided sample sequences

Estimates finite one- or two-sided limits only when the numerical samples demonstrate stable convergence.

Worked example

Removable discontinuity is a verified test case used by the calculation engine.

Assumptions and limitations

  • This version certifies finite numerical limits only.
  • Oscillatory, divergent or unequal two-sided behavior is rejected.
  • Numerical sampling is not a proof of a symbolic limit.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic numerical-calculus engine — Finite limit estimator with one-sided convergence checks.

Frequently asked questions

Can it detect a limit that does not exist?

It rejects common non-convergent cases when the numerical samples fail the convergence checks or the two sides disagree.

Are infinite limits supported?

Not in this certified version; it is intentionally limited to finite limits.

Related calculators

Derivative CalculatorEstimate a function derivative at a point with deterministic numerical refinement.Integral CalculatorCompute a finite definite integral with adaptive numerical refinement.